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# 3.1: One-Step Equations

Difficulty Level: At Grade Created by: CK-12

## Learning Objectives

At the end of this lesson, students will be able to:

• Solve an equation using addition.
• Solve an equation using subtraction.
• Solve an equation using multiplication.
• Solve an equation using division.

## Vocabulary

Terms introduced in this lesson:

equal
equation
isolate
linear equation

## Teaching Strategies and Tips

Use the introductory problem to motivate equivalent equations, since it can be solved two ways:

• The cost plus the change received is equal to the amount paid, $x + 22 = 100$.
• The cost is equal to the difference between the amount paid and the change, $x = 100 - 22$

Examples 1 and 2 are essentially the same; constant terms must be added to both sides to isolate $x$ on the left. Adding vertically can benefit students.

Solve $12 = -4 + x$.

Solution. To isolate $x$, add $4$ to both sides of the equation. Add vertically.

$12 & = -\cancel{4} + x\\+4 & = +\cancel{4}\\16 & = x$

The variable in Example 3 is not the usual $x$. Remind students that the letter of the variable does not matter. Additional Example.

Solve $-21=n+14$.

Hint: To isolate $n$, subtract $14$ from both sides of the equation.

In Examples 4-6, teachers may opt to solve the equations by adding the opposite in lieu of subtracting.

Example.

Solve $-17=x+8$.

Hint: To isolate $x$, add $-8$ to both sides of the equation. Add vertically.

$-17 & = x+\cancel{8}\\-8 & = -\cancel{8}\\-25 & = x$

Use Example 6 as an example of an equation with fractions. Remind students to find common denominators.

Point out in Example 8 that in general,

$\frac{ax}{b}=\frac{a}{b}x$

which will help students isolate $x$ in one step, multiplying by the reciprocal of $a/b$.

Note that the equation in Example 10 can be written in dollars or in cents:

• $5x=3.25$ ($x$ in dollars)
• $5x=325$ ($x$ in cents)

Although Examples 13 and 15 can be solved by making a table and Example 14 by guessing and checking, teachers are encouraged to help students setup and solve an equation of the type presented in the lesson.

## Error Troubleshooting

General Tip: After the constant term is canceled in a one-step equation, the variable must be carried down onto the next line. Remind students to write the $x =$.

General Tip: Students forget to perform the same operation on both sides of an equation. Have students use a colored pencil to write what they are doing to both sides of the equation.

Feb 22, 2012

Aug 22, 2014